Generating an area coverage vector

ABSTRACT

Certain examples described herein relate to generating a Neugebauer Primary area coverage (NPac) vector. In certain cases, a first plurality of Neugebauer Primaries (NPs) defined by a first NPac vector is determined, the first plurality of NPs defining a set of characteristics of a printing process. A second NPac vector, defining a second plurality of NPs, is generated based on the set of characteristics and a criterion relating to the printing process.

BACKGROUND

A printing system may be associated with a color space, defined bycolorants available to the printing system for deposition or applicationto a print medium. An example of a colorant color space is the Cyan,Magenta, Yellow, BlacK (CMYK) color space, wherein four variables areused in a subtractive color model to represent respective quantities ofcolorants. Examples of colorants include inks, dyes, pigments, paints,toners and powders.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features of the present disclosure will be apparent from thedetailed description which follows, taken in conjunction with theaccompanying drawings, which together illustrate, by way of example,features of the present disclosure, and wherein:

FIG. 1 is a schematic diagram of a printing system according to anexample;

FIG. 2 is a schematic diagram showing a representation of a NeugebauerPrimary area coverage vector according to an example;

FIG. 3 is a flow chart illustrating a method of generating a NeugebauerPrimary area coverage vector according to an example; and

FIG. 4 is a schematic diagram of a processor and a computer readablestorage medium with instructions stored thereon according to an example.

DETAILED DESCRIPTION

Color can be represented within print and display devices in a largevariety of ways. For example, in one case, a color as observed visuallyby an observer is defined with reference to a power or intensityspectrum of electromagnetic radiation across a range of visiblewavelengths. In other cases, a color model is used to represent a colorat a lower dimensionality. For example, certain color models make use ofthe fact that color may be seen as a subjective phenomenon, i.e.dependent on the make-up of the human eye and brain. In this case, a“color” may be defined as a category that is used to denote similarvisual perceptions; two colors are said to be similar if they produce asimilar effect on a group of people. These categories can then bemodelled using a lower number of variables.

Within this context, a color model may define a color space. A colorspace in this sense may be defined as a multi-dimensional space, with apoint in the multi-dimensional space representing a color value anddimensions of the space representing variables within the color model.For example, in a Red, Green, Blue (RGB) color space, an additive colormodel defines three variables representing different quantities of red,green and blue light. In a digital model, values for these quantitiesmay be defined with reference to a quantized set of values. For example,a color defined using an 8-bit RGB model may have three values stored ina memory, wherein each variable may be assigned a value between 0 and255. Other color spaces include: a Cyan, Magenta, Yellow and Black(CMYK) color space, in which four variables are used in a subtractivecolor model to represent different quantities of colorant or printingfluid, e.g. for a printing system; the International Commission onIllumination (CIE) 1931 XYZ color space, in which three variables (‘X’,‘Y’ and ‘Z’ or ‘tristimulus values’) are used to model a color; the CIE1976 (L*, a*, b*—CIELAB or ‘LAB’) color space, in which three variablesrepresent lightness (‘L’) and opposing color dimensions (‘a’ and ‘b’);and the Yu‘v’ color space, in which three variables represent theluminance (‘Y’) and two chrominance dimensions (u′ and v′).

Other color spaces include area coverage spaces, such as the NeugebauerPrimary area coverage (NPac) color space. An NPac vector in the NPaccolor space represents a statistical distribution of NeugebauerPrimaries (NPs) over an area of a halftone. In a simple binary(bi-level, i.e. two drop states: “drop” or “no drop”) printing system or“printer”, an NP may be one of 2^(k)−1 combinations of k printing fluidswithin the printing system, or an absence of printing fluid (resultingin 2^(k) NPs in total). A colorant or printing fluid combination asdescribed herein may be formed of one or multiple colorants or printingfluids. For example, if a bi-level printing device uses CMY printingfluids there can be eight NPs. These NPs relate to the following: C, M,Y, CM, CY, MY, CMY, and W (white or blank indicating an absence ofprinting fluid). An NP may comprise an overprint of two availableprinting fluids, such as a drop of magenta on a drop of cyan (for abi-level printer) in a common addressable print area (e.g. a printable“pixel”). An NP may be referred to as a “pixel state”.

In multi-level printers, e.g. where print heads are able to deposit Ndrop levels, an NP may include one of N^(k)-1 combinations of k printingfluids, or an absence of printing fluid (resulting in N^(k) NPs intotal). For example, if a multi-level printer uses CMY printing fluidswith four different drop states (“no drop”, “one drop”, “two drops” or“three drops”), available NPs can include C, CM, CMM, CMMM, etc.

An NPac color space may provide a large number of metamers. Metamerismis the existence of a multitude of combinations of reflectance andemission properties that result in the same perceived color for a fixedilluminant and observer. Colors that are perceived as the same color inthis way may be called ‘metamers’.

Each NPac vector may therefore define a probability distribution forcolorant or printing fluid combinations for each pixel in the halftone(e.g. a likelihood that a particular colorant or printing fluidcombination is to be placed at each pixel location in the halftone). Inthis manner, a given NPac vector defines a set of halftone parametersthat can be used in the halftoning process to map a color to NPacvectors to be statistically distributed over the plurality of pixels fora halftone. Moreover, the statistical distribution of NPs to pixels inthe halftone serves to control the colorimetry and other printcharacteristics of the halftone.

Spatial distribution of NPs according to the probability distributionspecified in the NPac vector may be performed using a halftone method.Examples of suitable halftoning methods include matrix-selector-basedParallel Random Area Weighted Area Coverage Selection (PARAWACS)techniques and techniques based on error diffusion. An example of aprinting system that uses area coverage representations for halftonegeneration is a Halftone Area Neugebauer Separation (HANS) pipeline.

Certain examples described herein relate to generating a vector in areacoverage space, e.g. generating a Neugebauer Primary area coverage(NPac) vector in the NPac color space. The vector may be generated toupdate an original vector in a color lookup table, e.g. corresponding toan entry stored in the color lookup table. The color lookup table maymap between color spaces, storing such mappings as entries in the colorlookup table. For example, the color lookup table 150 may mapcolorimetric values in a color space with vectors in area coveragespace.

A color lookup table may be generated by defining mappings betweenparticular locations in two respective color spaces, and storing themappings as entries, or “nodes”, in a data structure, i.e. the colorlookup table. Intermediate nodes in the color lookup table (e.g. entriesin the color lookup table corresponding to respective locations in acolor space that are between particular locations in the color spacethat have a defined mapping) may be interpolated based on surroundingnodes that are associated with a defined mapping. For example, a regularsampling (e.g. of 17³ or 9⁴ entries) may be taken from the color lookuptable and interpolated using an interpolation sequence, e.g. rangingfrom a simple Delaunay tessellation to more advanced methods.

Such interpolation methods may vary in which surrounding nodes are usedto interpolate a given new node, however many use a form of convexcombination or barycentric coordinate computation and may thereforeproduce NPac vectors that use the union of sets of colorantcombinations, e.g. NPs, defined by each of the NPac vectorscorresponding to the nodes used to interpolate the new node.

According to examples described herein, generating the vector in areacoverage space is based on a criterion relating to a printing process.For example, an imaging metric corresponding to the criterion may beapplied when generating the vector. In this way, the color lookup tablemay be updated or altered based on the criterion, for example byupdating vectors in area coverage space corresponding to entries in thecolor lookup table with vectors in area coverage space generated basedon the criterion.

The criterion may relate to overprinting in a print output generatedusing a printing process. In examples, the criterion may compriseincreasing overprinting in the print output. For example,single-colorant NPs present in an NPac vector may have at least part ofthe associated area coverage contributions ‘transferred’ to an areacoverage contribution associated with a multi-colorant NP. As anexample, if NPs of C and M are present in an NPac vector, at least partof the associated contributions of these NPs may be transferred to anarea coverage contribution associated with a multi-colorant NP (CM) inthe generated NPac vector, according to examples.

Conversely, in other examples the criterion relating to overprintingcomprises decreasing overprinting in the print output. In this case,area coverage contributions of multi-colorant NPs (e.g. CM) may be atleast partly transferred to area coverage contributions associated withsingle-colorant NPs (e.g. C and M).

The criterion may additionally or alternatively relate to whitespace inthe print output generated by the printing process, which is discussedin examples below. The imaging metric applied, based on the criterionrelating to the printing process, may be different in different regionsof the color lookup table. For example, vectors in area coverage spacemay be generated based on different criteria depending on the entry inthe color lookup table that the generated vector is to correspond to,e.g. depending on the colorimetric value in a color space that thegenerated vector is to map to. In certain examples, there may bedifferent versions of a color lookup table updated from an originalcolor lookup table using generated NPac vectors as described herein. Forexample, a version of the color lookup table may be updated based on thecriterion comprising increasing overprinting. Another version of thecolor lookup table may be updated based on the criterion comprisingdecreasing overprinting. The different versions may be used depending onthe printing process, e.g. the version based on decreasing overprintingmay be used when printing lines onto a print target.

Updating NPac vectors corresponding to entries in a color lookup tablewith NPac vectors generated according to examples described herein mayimprove smoothness of the print output. For example, if an NPac vectoris updated to increase area coverage contributions of multi-colorantNPs, i.e. that overprint, contrast between different NPs may be lowered.Therefore, the overall printed image, e.g. halftone pattern, may besmoother). In some cases, criteria of both increasing overprinting anddecreasing whitespace, e.g. maximizing overprinting and minimizingwhitespace, may decrease grain in color separations. Grain may beassociated with local contrast between units, e.g. drops, of colorantcombinations, and how such local contrast is distributed (e.g. based ona standard deviation of color or lightness differences). Generating anNPac vector based on this combination of imaging metrics may result inthe NPac vector comprising NPs that have a lower contrast between eachother compared to the NPs of the original NPac vector. This maytherefore contribute to a lower grain in the print output.

In other cases, updating NPac vectors corresponding to entries in acolor lookup table with NPac vectors generated according to examplesdescribed herein may improve line definition in a print output. Forexample, if an NPac vector is updated to increase area coveragecontributions of single-colorant NPs, i.e. that print side-by-side, moreof the print target, e.g. print media, may be occupied using the sameamount of print material for a given colorant.

FIG. 1 shows a printing system 100 according to an example. Certainexamples described herein may be implemented within the context of thisprinting system.

The printing system 100 may be a 2D printing system such as an inkjet ordigital offset printer, or a 3D printing system, otherwise known as anadditive manufacturing system. In the example of FIG. 1, the printingsystem 100 comprises a printing device 110, a memory 120, and a printcontroller 130. The print controller 130 may be implemented usingmachine readable instructions and suitably programmed or configuredhardware, e.g. circuitry.

The printing device 100 is arranged to apply a print material to a printtarget in a printing process, for example to produce a print output 140.The print output 140 may, for example, comprise colored printing fluidsdeposited on a substrate. The printing device 110 may comprise an inkjetdeposit mechanism, which may e.g. comprise a nozzle to deposit printingfluid on the substrate. The inkjet deposit mechanism may includecircuitry to receive instructions associated with depositing printingfluid. In 2D printing systems, the substrate may be paper, fabric,plastic or any other suitable print medium.

In 3D printing systems, the print output 140 may be a 3D printed object.In such systems, the substrate may be a build material in the form of apowder bed comprising, for example, plastic, metallic, or ceramicparticles. Chemical agents, referred to herein as “printing agents”, maybe selectively deposited onto a layer of build material. In one case,the printing agents may comprise a fusing agent and a detailing agent.In this case, the fusing agent is selectively applied to a layer inareas where particles of the build material are to fuse together, andthe detailing agent is selectively applied where the fusing action is tobe reduced or amplified. In some examples, colorants may be deposited ona white or blank powder to color the powder. In other examples, objectsmay be constructed from layers of fused colored powder.

The memory 120 stores a color lookup table 150 to map between colorspaces. For example, the color lookup table 150 may map colorimetricvalues with vectors in the area coverage space. The color lookup table150 may map RGB or CMYK color values to NPac vectors, for example. Insome examples, the color lookup table 150 maps XYZ, LAB or any othercolor space used to specify the device color space. Where the vectorscomprise NPac vectors, the color lookup table 150 may be referred to asa “HANS lookup table”. When an RGB mapping is used, the HANS lookuptable may comprise 17³ entries. When a CMYK mapping is used, the HANSlookup table may comprise 9⁴ entries.

The print controller 130 is arranged to generate a vector in areacoverage space, the vector defining a statistical distribution ofcolorant combinations over an area of a halftone. In examples, thegenerated vector is an NPac vector.

As part of generating the vector, the print controller 130 is arrangedto select from the color lookup table 150 a first vector in areacoverage space. For example, the first vector may correspond to an entryin the color lookup table 150. The color lookup table 150 may map toarea coverage space, for example from a first color space. The printcontroller 150 may therefore select an entry in the color lookup table150 and select the corresponding vector in area coverage space, the saidcorresponding vector being the first vector. In examples, the memory 120may store the first vector corresponding to an entry in the color lookuptable 150. The first vector may define a statistical distribution ofcolorant combinations over an area of a halftone. In examples, the firstvector comprises an NPac vector. As described, the color lookup table150 may comprise a HANS lookup table, and the first vector may thereforecomprise the NPac vector corresponding to an entry in the HANS lookuptable.

As part of generating the vector, the print controller 130 is alsoarranged to determine a first plurality of colorant combinations basedon the first vector. The first plurality of colorant combinations definea set of colorants associated with the printing process. For example,the set of colorants associated with the printing process may be a setof colorants printable by the printing system 100. The printing system100 may be able to print more colorants than those in the set ofcolorants defined by the first plurality of colorant combinations. Forexample, the set of colorants defined by the first plurality of colorantcombinations may be a subset of a complete set of available colorants,wherein the complete set of available colorants defines all colorantsprintable by the printing system 100.

A colorant may be otherwise referred to as a “printing fluid”. Acolorant may correspond to a given base color, where other colors may beformed from combinations of colorants. Examples of base colors include,but are not limited to, cyan, magenta, yellow, red, green and blue andblack. The number of colorants in a given set of colorants is less thanthe number of possible colorant combinations, e.g. NPs, based on thegiven set of colorants.

The first vector may define, for each of the first plurality of colorantcombinations, a likelihood that a given colorant combination in thefirst plurality of colorant combinations is to be placed at a givenlocation in an image, e.g. a given pixel location in a halftone. Forexample, the first vector may comprise a plurality of components, eachcomponent corresponding to a colorant combination in the first pluralityof colorant combinations. A given component of the first vector maycomprise a value corresponding to a likelihood that a colorantcombination corresponding to the given component is to be placed at thegiven location in the image. In examples where the first vector is anNPac vector, the first plurality of colorant combinations may correspondto a first plurality of NPs.

As part of generating the vector in area coverage space, the printcontroller 130 generates a second vector in area coverage space defininga second plurality of colorant combinations. For example, the secondvector may have components corresponding to colorant combinationscomprised in the second plurality of colorant combinations. Generationof the second vector is based on the set of colorants defined by thefirst plurality of colorant combinations. This generation of the secondvector is also based on a criterion relating to the printing process.For example, the colorant combinations used as the second plurality ofcolorant combinations, and the corresponding values (e.g. relating toarea coverage) comprised in the second vector, may be determined basedon the criterion.

In examples, as part of generating the vector, the print controller 130is also arranged to determine an intermediate plurality of colorantcombinations based on the set of colorants defined by the firstplurality of colorant combinations. As an illustrative example, thefirst vector could comprise three components corresponding to threecolorant combinations: [C, CM, YY]. In this example, the first pluralityof colorant combinations would therefore comprise C, CM, and YY and theset of colorants defined by the first plurality of colorant combinationswould comprise C, M, and Y. The print controller 130 may determine theintermediate plurality of colorant combinations from the base colorantsC, M, and Y, i.e. based on the set of colorants defined by the firstplurality of colorant combinations.

The intermediate plurality of colorant combinations may comprise some orall the colorant combinations in the first plurality of colorantcombinations. The intermediate plurality of colorant combinations mayadditionally or alternatively comprise a colorant combination notpresent in the first plurality of colorant combinations. For example,the print controller 130 may combine colorants in the set of colorantsdefined by the first plurality of colorant combinations to generate acolorant combination not present in the first plurality of colorantcombinations. Such generated colorant combinations may be included inthe intermediate plurality of colorant combinations, e.g. in addition tothe colorant combinations comprised in the first plurality of colorantcombinations. Returning to the illustrative example, the printcontroller 130 may combine the colorants M and Y from the set ofcolorants to generate a colorant combination MY not present in the firstplurality of colorant combinations (C, CM, and YY).

In alternative examples, the print controller 130 may determine theintermediate plurality of color combinations by selecting combinationsof the colorants in the set of colorants from a plurality of colorantcombinations associated with the printing process. For example, theplurality of colorant combinations associated with the printing processmay be a plurality of colorant combinations that are printable by theprinting system 100. In some examples the plurality of colorantcombinations associated with the printing process may be a predeterminedplurality of colorant combinations, i.e. all colorant combinations thatare printable by the printing system 100. All the colorant combinationsthat are printable by the printing system 100 may be termed a “valid”set of colorant combinations. Therefore, the print controller 130 mayselect colorant combinations in the valid set of colorant combinationsthat are combinations of the colorants in the set of colorants. Again,returning to the illustrative example, combinations of the colorants C,M, and Y may be selected from the valid set of colorant combinations,e.g. which may comprise CC, CY, YC, MM, MY, YM. In examples, colorantcombinations in the valid set of colorant combinations that comprisecolorants not present in the set of colorants defined by the firstplurality of colorant combinations are not selected.

In examples, the criterion relating to the printing process relates tooverprinting in a print output generated using the printing process. Anoverprint may comprise a unit (e.g. a drop) of one available colorantdeposited on top of a unit of another available colorant in a commonaddressable print area (e.g. a pixel). For example, the colorantcombination CM may correspond to an overprint of one drop of magenta (M)on top of one drop of cyan (C). In some cases, the criterion maycomprise increasing overprinting. In certain cases, the criterioncomprises maximizing overprinting. Maximizing overprinting maycorrespond to increasing the amount of overprinting in the print output,e.g. increasing the proportional area of the print output that isoverprinted, subject to constraints. Examples of such constraints arediscussed further below. As an illustrative example, to increaseoverprinting when generating the second vector in area coverage space,the print controller 130 may use overprint colorant combinations fromthe intermediate plurality of colorant combinations. Additionally, oralternatively, the print controller 130 may give a larger area coveragevalue to components of the second vector that correspond to overprintcolorant combinations, relative to components of the second vector thatdo not correspond to overprint colorant combinations.

In other cases, the criterion comprises decreasing overprinting. Thismay correspond to increasing side-by-side printing of colorants.Side-by-side printing may involve printing units of colorants next toone another rather than on top of one another as in overprinting (e.g.depositing a drop each of C and M next to each other in an addressableprint area as opposed to a drop of M on top of one drop of C). In theseexamples, the print controller 130 may use non-overprint colorantcombinations from the intermediate plurality of colorant combinations,e.g. single-colorant combinations. Additionally, or alternatively, theprint controller 130 may give a larger area coverage value to componentsof the second vector that correspond to single-colorant combinations,relative to components of the second vector that correspond to overprintcolorant combinations. In examples the criterion comprises decreasingoverprinting, which may correspond to decreasing the amount ofoverprinting in the print output, e.g. decreasing the proportional areaof the print output that is overprinted, subject to constraints. Incertain cases, the criterion comprises minimizing overprinting.

In examples, the criterion may additionally or alternatively relate towhitespace in the print output generated by the printing process. Forexample, the criterion may comprise increasing or decreasing whitespacein the print output. “Whitespace” may be considered a portion of a printtarget or image, e.g. the print output, which does not have printmaterial, e.g. a colorant, applied to it. Therefore, decreasingwhitespace may corresponding to reducing the proportion of the printtarget that is left blank. In some cases the criterion comprisesminimizing whitespace, for example decreasing the amount of whitespaceas much as possible subject to constraints. As an illustrative example,to decrease whitespace when generating the second vector in areacoverage space, the print controller 130 may give a smaller areacoverage to a component of the second vector that corresponds to a blank(W) colorant combination (i.e. indicating an absence of colorant e.g.printing fluid), relative to other components of the second vector thatcorrespond to non-blank colorant combinations.

In examples, the generating of the second vector by the print controller130 is based on an adjustment of a relation involving colorantcombinations in a given set of colorant combinations in an intermediateplurality of colorant combinations, and corresponding area coverages.The intermediate plurality of colorant combinations may comprise thevalid set of colorant combinations in some examples. In other examples,the intermediate plurality of colorant combinations may comprise asubset of the valid set, e.g. colorant combinations generated orselected, as described in examples above. The relation may involve acertain number of colorant combinations corresponding to the number ofcomponents in the second vector to be generated. The relation mayinclude colorant combinations in the given set of colorant combinations,and corresponding area coverages, as variables. Therefore, differentinput colorant combinations, selected from the set of colorantcombinations, and corresponding area coverages, may give differentoutputs from the relation. In examples, adjusting the relation mayinclude improving the relation between colorant combinations in thegiven set of colorant combinations, e.g. optimizing the relation. Therelation may be considered a function of the variable colorantcombinations and corresponding area coverages, e.g. an objectivefunction.

A metric based on the criterion may be applied to the given set ofcolorant combinations. For example, colorant combinations may beweighted differently in the relation, with weightings dependent on thecriterion. As an example, if the criterion were to increaseoverprinting, and adjusting the relation comprised reducing an outputvalue of the function of the variable colorant combinations andcorresponding area coverages, e.g. minimizing an objective function, thecolorant combinations may be weighted to penalize blank space andsingle-colorant combinations relative to overprint combinations. In thisway, adjustment of the relation may favor colorant combinations that areassociated with the criterion, e.g. overprint combinations when thecriterion comprises increasing overprinting. The metric applied to thegiven set of colorant combinations may be hierarchical. For example, ifthe criterion were to increase overprinting, blank colorant combinationsmay be penalized more than single-colorant combinations, which in turnmay be penalizes relative to overprint combinations.

In some examples, a further metric based on the set of colorants definedby the first plurality of colorant combinations is applied to theintermediate plurality of colorant combinations. For example, colorantcombinations may be weighted differently in the relation, withweightings dependent on colorants comprised in the colorantcombinations. In examples, colorant combinations in the intermediateplurality of colorant combinations that comprise colorants not in theset of colorants may be weighted to penalize those colorantcombinations. This may be an alternative to deriving a subset of thevalid set of colorant combinations, as described above in examples. Forexample, the valid set of colorant combinations may be used as theintermediate plurality of colorant combinations, and weightings may beapplied to the colorant combinations in the valid set, the weightingsbased on whether a given colorant combination comprises colorants notpresent in the first plurality of colorant combinations.

In examples, the adjustment of the relation comprises a constraintwherein a second colorant-use vector, determinable based on the secondplurality of colorant combinations and corresponding area coverages usedto generate, i.e. defining, the second vector, is equivalent to a firstcolorant-use vector determined based on the colorant combinations andcorresponding area coverages defined by the first vector. A colorant-usevector may comprise components corresponding to individual colorants,where values of the components correspond respectively to the amount ofthe corresponding colorant used relative to the other colorantsrepresented in the colorant-use vector. Component values of acolorant-use vector may therefore be determined based on colorantcombinations and corresponding relative area coverages, e.g. from avector in area coverage space, such as an NPac vector. In certain cases,the first colorant-use vector is determined as described above, and thecolorant combinations and corresponding area coverages selectable togenerate the second vector are those that would give a colorant-usevector equivalent to the first colorant-use vector. Equivalentcolorant-use vectors may comprise the same value per component, whereinthe vector components correspond respectively to the amount of thecorresponding colorant used relative to the other colorants representedin the colorant-use vector, as described above.

In examples, a set of colorant combinations and corresponding areacoverages that improve the relation are selected as components of thesecond vector. For example, where the relation is considered a function,e.g. an objective function, of the variable colorant combinations andcorresponding area coverages, and adjusting the relation comprisesminimizing the objective function, e.g. subject to constraints, thecolorant combinations and corresponding area coverages selected to formthe second vector may be those that minimize an output of the objectivefunction, e.g. give the minimum output value possible based on theavailable input variables. As an example, for a colorant-use vector of[Cyan 50%, Magenta 50%], and the criterion comprising minimizingwhitespace, the set of colorant combinations and corresponding areacoverages that gives the minimum output value may be 01:0.5, M1:0.5,wherein C1 and M1 denote one unit, or ‘drop’, of Cyan and Magentacolorant, respectively. The second vector [01:0.5, M1:0.5] comprisingthis set of colorant combinations and corresponding area coverages ascomponents gives an output value of zero (i.e. the minimum) for theobjective function, as there in no blank W component present in thesecond vector. If the criterion were to maximize whitespace, the set ofcolorant combinations and corresponding area coverages that gives themaximum output value may be CCMM:0.25, W:0.75, where 0, 1 or 2 units ofeach colorant are possible. This set of colorant combinations andcorresponding area coverages gives an output value of 0.75 for theobjective function, and may be selected as the components of the secondvector.

In examples, the print controller 130 is to update the first vector withthe second vector in the color lookup table 150 stored in the memory120. For example, the print controller 130 may update the entry in thecolor lookup table 150 that maps to the first vector to instead map tothe second vector. The color mapping represented by the color lookuptable 150 may be applied to print job data, for example in a printingoperation performed by the printing system 100. In examples, the firstvector may be adjusted to correspond to the second vector. In otherexamples, the first vector may be replaced by the second vector, e.g.the first vector may be deleted from a memory location and the secondvector stored at the memory location.

FIG. 2 shows an example NPac vector 200 for use in a CMY imaging system.The NPac vector 200 may be a generated NPac vector resulting from amethod performed in accordance with examples described herein. Thisexample shows a three-by-three pixel area 210 of a print output whereall pixels have the same NPac vector: vector 200. The NPac vector 200defines the probability distributions for each NP for each pixel, forexample a likelihood that NP_(x) is to be placed at the pixel location.Hence, in the example print output there is one pixel of White (W)(235); one pixel of Cyan (C) (245); two pixels of Magenta (M) (215); nopixels of Yellow (Y); two pixels of Cyan+Magenta (CM) (275); one pixelof Cyan+Yellow (CY) (255); one pixel of Magenta+Yellow (MY) (205); andone pixel of Cyan+Magenta+Yellow (CMY) (265). Generally, the printoutput of a given area is generated such that the probabilitydistributions set by the NPac vectors of each pixel are fulfilled. Forexample, the NPac vector may be effected by a halftone stage thatimplements the spatial distribution of colorants combinations defined bythe vector, e.g. via a series of geometric shapes such as dots ofpredetermined sizes being arranged at predetermined angles. As such, anNPac vector is representative of the colorant overprint statistics of agiven area. Although a CMY system is used for ease of explanation, otherimaging systems may be used.

FIG. 3 shows a method 300 of generating a Neugebauer Primary areacoverage (NPac) vector according to an example. In some examples, themethod 300 is performed by a print controller such as the printcontroller 130 of FIG. 1. The print controller may perform the methodbased on instructions retrieved from a computer-readable storage medium.The printing system may comprise the printing system 100 of FIG. 1.

At item 310, a first plurality of Neugebauer Primaries (NPs) isdetermined. The first plurality of NPs is defined by a first NPacvector. For example, the first NPac vector may comprise componentscorresponding respectively to NPs in the first plurality of NPs. Thefirst NPac vector may be selected in examples, e.g. from a HANS lookuptable, or from a memory based on a corresponding entry in the HANSlookup table. The HANS lookup table may be stored in the memory. Thememory may be comprised in or separate from the printing system.

The first plurality of NPs define a set of characteristics of a printingprocess. The printing process may be performable by the printing system100, and may comprise applying print material to a print target. Inexamples, the set of characteristics comprises a set of colorantsassociated with the printing process. For example, the set of colorantsmay comprise colorants that are printable in the printing process, e.g.by the printing system. The set of colorants may be combined to giveeach NP in the first plurality of NPs.

At item 320, a second NPac vector, defining a second plurality of NPs,is generated based on the set of characteristics and a criterionrelating to the printing process. Example criterions include thosepreviously described with reference to the printing system 100 ofFIG. 1. For example, the criterion may relate to overprinting orwhitespace in a print output generated using the printing process. Forexample, the criterion may comprise increasing or decreasingoverprinting and/or increasing or decreasing whitespace in the printoutput. In some cases, determining the intermediate plurality of NPs mayalso be based on the criterion. For example, certain NPs may be excludedor not selected based on the criterion to be applied at item 320. As anexample, if the criterion comprises increasing overprinting,single-colorant NPs may be omitted from the intermediate plurality ofNPs, e.g. when determining the intermediate plurality of NPs based onthe set of characteristics, e.g. the set of colorants. Similarly,generating the second NPac vector based on the set of characteristicsmay correspond to examples previously described with reference to theprinting system 100 of FIG. 1. For example, the second plurality of NPsmay be determined from an intermediate plurality of NPs based on the setof characteristics, e.g. the set of colorants defined by the firstplurality of NPs. The intermediate plurality of NPs may be apredetermined plurality of NPs, e.g. the valid set of NPs, as previouslydescribed, and determining the second plurality of NPs may compriseweighting NPs in the predetermined plurality of NPs. Weightings maydepend on whether a given NP comprises a colorant not present in the setof colorants.

In some examples, the intermediate plurality of NPs is determined, basedon the set of characteristics. For example, where the set ofcharacteristics is a set of colorants, the colorants in the set ofcolorants may be combined to give the intermediate plurality of NPs.Determining the intermediate plurality of NPs may therefore comprisegenerating colorant combinations from the set of colorants. A limit maybe implemented in the generation of colorant combinations from the setof colorants, for example a maximum number of different colorantscombinable in a colorant combination, and/or a maximum number of units(e.g. drops) represented in a colorant combination. Such limits mayallow the generation of colorant combinations from the set of colorantsto not continue ad infinitum. In examples where the first plurality ofNPs does not comprise a blank NP, e.g. W, the blank NP is not selectedwhen determining the intermediate plurality of NPs.

In alternative examples, determining the intermediate plurality of NPscomprises selecting NPs from the predetermined plurality of NPsassociated with the printing process. For example, the predeterminedplurality of NPs associated with the printing process may comprise allNPs printable or “valid” in the printing process. The NPs selected fromthe predetermined plurality of NPs may correspond to combinations ofcolorants in the set of colorants defined by the first plurality of NPs.For example, NPs comprising a colorant not present in the set ofcolorants may not be selected when determining the intermediateplurality of NPs.

In examples, the method 300 involves determining a first colorant-usevector based on the first plurality of NPs and corresponding areacoverages defined by the first NPac vector. As described, a colorant-usevector may comprise components corresponding to individual colorants,where values of the components correspond respectively to the amount ofthe corresponding colorant used relative to the other colorantsrepresented in the colorant-use vector. Component values of acolorant-use vector may therefore be determined based on NPs andcorresponding relative area coverages defined by an NPac vector.

The method 300 may also include generating the second NPac vector suchthat a second colorant-use vector, determinable based on the secondplurality of NPs and corresponding area coverages defined by, i.e. usedto generate, the second NPac vector, is equivalent to the firstcolorant-use vector.

In examples, the method 300 may involve applying an imaging metric tothe intermediate plurality of NPs, the imaging metric corresponding tothe criterion. The intermediate plurality of NPs may comprise the secondplurality of NPs. A relation between NPs in a given set of NPs in theintermediate plurality of NPs may be determined as part of the method300, which may also include determining the second plurality of NPs as aset of NPs from the intermediate plurality of NPs, and correspondingarea coverages, based on the relation, e.g. that improve or optimize therelation. As described above, the intermediate plurality of NPs maycomprise the valid set of NPs, or a subset thereof, or a set of NPsgenerated based on the set of characteristics, e.g. colorants.

For example, applying an imaging metric to the intermediate plurality ofNPs may comprise weighting NPs in the intermediate plurality of NPsdifferently for input to the relation, with weightings dependent on thecriterion. As an example, if the criterion comprises increaseoverprinting, and improving the relation comprises reducing an output ofan objective function within constraints, the NPs in the intermediateplurality of NPs may be weighted to penalize blank space andsingle-colorant NPs relative to overprint NPs. In this way, improvingthe relation may favor NPs that are associated with the criterion, e.g.overprint NPs if the criterion comprises increasing overprinting. Themetric applied to the given set of colorant combinations may behierarchical. For example, if the criterion comprises increasingoverprinting, a blank NP may be penalized more than single-colorant NPs,which in turn may be penalized relative to overprint NPs.

Area coverages corresponding to NPs, e.g. in an NPac vector, maycomprise a value in a range of 0 to 1, or [0, 1], since the areacoverages represent probabilities. If the criterion comprises increasingoverprinting, applying the imaging metric to the intermediate pluralityof NPs may comprise giving the blank NP (e.g. W) a relative weight of10000, for example. Single-colorant NPs may be given a relative weightof 100, and overprint or multi-colorant NPs may be given a relativeweight of 1. These relative weightings may therefore produce a relationbetween a given set of NPs in the intermediate plurality of NPs, e.g. anobjective function, that penalizes whitespace most, followed bysingle-colorant NPs and has nominal values for multi-colorant NPs thataccord with the criterion of increasing overprinting. In this example,an error from 0.1% of blank space may be 1, while an error of 1 would beachieved if a single multi-ink NP were at 100% coverage. Hence, outputvalues corresponding to blank NPs may weigh orders of magnitude morethan those caused by NPs that are in accordance with the criterion.

In examples, the method 300 comprises generating the second NPac vectormay include generating the second NPac vector using the second pluralityof NPs and corresponding area coverages determined to improve therelation.

In examples, determining the relation between a given set of NPs in theintermediate plurality of NPs is based on constraints. The constraintsmay include a second colorant-use vector, determinable based on thesecond plurality of NPs and corresponding area coverages used togenerate, i.e. define, the second NPac vector, corresponding to, forexample being equivalent to, a first colorant-use vector determinedbased on the first plurality of NPs and corresponding area coveragesdefined by the first NPac vector. In certain cases, the firstcolorant-use vector is determined as described above, and the secondplurality of NPs and corresponding area coverages selectable to generatethe second vector are those that would give a colorant-use vectorequivalent to the first colorant-use vector. This constraint maycorrespond to an equality condition when improving the relation.

The constraints may include a predetermined minimum area coverage ofeach NP defined by, i.e. used to generate, the second NPac vector. Forexample, as area coverages in an NPac vector represent probabilities, aminimum area coverage value of zero may be set as a constraint. This maymean that negative area coverages are not allowed in the generatedsecond NPac vector. In other examples, the predetermined minimum areacoverage may be greater than zero. This may result in fewer NPs used togenerate, and thus defined by, the second NPac vector, e.g. compared tothe number of NPs associated with the first NPac vector. This constraintmay correspond to an inequality condition when improving the relation.

Similarly, the constraints may include a predetermined maximum areacoverage of each NP defined by, i.e. used to generate, the second NPacvector. For example, as area coverages in an NPac vector representprobabilities, a maximum area coverage value of one may be set as aconstraint. This may mean that any area coverage value, corresponding toan NP, in the generated second NPac vector may not exceed the print areaaddressable by the NPac vector. This constraint may correspond to aninequality condition when improving the relation.

The constraints may include a predetermined total area coverage of theNPs defined by, i.e. used to generate, the second NPac vector. Forexample, a sum of all area coverages in the generated second NPac vectorequivalent to a maximum possible probability, e.g. 1, may be set as aconstraint. This constraint may correspond to an equality condition whenimproving the relation.

Improving the relation between NPs in the given set of NPs in theintermediate plurality of NPs, i.e. when determining the secondplurality of NPs, may comprise applying a linear programming (LP)method, a random sample consensus (RANSAC) method, or a Monte Carlomethod.

For example, linear programming may be implemented by defining therelation between the given set of NPs in the intermediate plurality ofNPs as a linear objective function. The given set of NPs may bevariables in the linear objective function that can each take a valuecorresponding to an NP in the intermediate plurality of NPs.Corresponding area coverages for the given set of NPs may also bevariables in the linear objective function. The linear objectivefunction may be subject to the constraints described above. LPtechniques may involve finding values of the variables of the linearobjective function that improve, e.g. increase or decrease, an outputvalue of the linear objective function within the constraints. Afeasible region or solution space, e.g. a superset of all sets of valuesof the variables that satisfy the constraints, may be defined by theconstraints that the linear objective function is subject to. Thesolution space of an LP technique may be a convex polytrope defined byconvex constraints, and the LP technique may involve metric minimizationsubject to said convex constraints.

In alternative examples, the solution space define by the constraints,e.g. a convex hull (defined by the inequality constraints) intersectedwith hyperplanes (defined by the equality constraints), may be sampledor traversed while evaluating the objective function to improve, e.g.optimize, the relation analytically.

RANSAC or Monte Carlo techniques may additionally or alternatively beimplemented to take (pseudo-)random samples of variable values, e.g.which are generated. Each potential set of variable values may becompared to the constraints described above, and the objective functionmay be evaluated.

As an illustrative example of the present method 300 of generating aNeugebauer Primary area coverage (NPac) vector, a first NPac vector maycomprise NPs having the following area coverages: [YYY: 0.152859, mYY:0.486241, mYYY: 0.00840452, YYa: 0.0715979, YYYa: 0.00123757, YYN:0.043207, RR: 0.19126100, RRR: 0.0451916]. A first plurality of NPsdefined by the first NPac vector may be determined at item 310 as: YYY,mYY, mYYY, YYa, YYYa, YYN, RR, and RRR. The first plurality of NPsdefine a set of characteristics, e.g. a set of colorants: m, a, Y, R, N.In this example, an intermediate plurality of NPs may be determinedbased on the set of characteristics m, a, Y, R, N. For example, theintermediate plurality of NPs may include NPs such as YR and YN that arenot in the first plurality of NPs. The intermediate plurality of NPs mayalso include the first plurality of NPs defined by the first NPacvector. For example, the intermediate plurality of NPs may comprise alarger set of valid NPs, i.e. NPs printable by a printing system, thanthe first plurality of NPs. The intermediate plurality of NPs maycomprise a subset of a larger valid set of NPs, i.e. comprising all NPsprintable by the printing system. In this example, a second NPac vectormay be generated, at item 320, using NPs from the intermediate pluralityof NPs, based on a criterion relating to the printing process. In thisexample, the criterion comprises increasing overprinting. In thisexample, generating the second NPac vector based on the set ofcharacteristics comprises determining the intermediate plurality of NPs,from which the second plurality of NPs can be chosen to generate thesecond NPac vector based on the criterion. In other examples, theintermediate plurality of NPs may comprise a predetermined plurality ofNPs (e.g. the valid set of NPs) and generating the second NPac vectorbased on the set of characteristics comprises selecting the secondplurality of NPs from the intermediate plurality of NPs based on the setof characteristics in parallel with the criterion. For example, acolorant metric, based on the set of characteristics (e.g. colorants)defined by the first plurality of colorant combinations may be appliedto the intermediate plurality of NPs (or colorant combinations).

Continuing the example, an imaging metric corresponding to the criterionmay be applied to the intermediate plurality of NPs, e.g. to weight theNPs according to their correspondence with the criterion. A relationbetween a given set of NPs in the intermediate plurality of NPs may bedetermined and then improved to determine a ‘solution’ comprising a setof NPs from the intermediate plurality of NPs and corresponding areacoverages. In this example, the improving is performed using an LPtechnique, as described, and constrained by the two inequalityconditions and two equality conditions previously described. The‘solution’ set of NPs and corresponding area coverages may be used inthis example to generate the following second NPac vector: [mY:0.451717256667, Ya: 0.029907206667, YN: 0.021742868333, YR:0.1411030675, YYYR: 0.334065469167, mmYYRRaaN: 0.021464131667]. Thesecond NPac vector comprises no NP corresponding to a single colorant(e.g. the NPs YYY, RR, RRR of the first NPac vector are not present inthe second NPac vector) in accordance with the criterion to increaseoverprinting. Therefore, no pixel in the halftone uses Yellow on itsown, but all instead combine yellow with other colorants (e.g. a, R, andN). This may reduce contrast in the print output since all NPs are of amore similar lightness in the second NPac vector than in the first NPacvector.

In this illustrative example, the first NPac vector corresponds to anentry, or “node”, in a color lookup table that maps from the coordinate(240, 64, 0) in RGB color space. As described, the color lookup tablemay be stored in a memory accessible by a print controller comprised inthe printing system. The first NPac vector may be updated with thegenerated second NPac vector in the color lookup table. In this example,the generated second NPac vector replaces the first NPac vector ascorresponding to the node in the color lookup table that maps from thecoordinate (240, 64, 0) in RGB color space. Therefore, the coordinate(240, 64, 0) in RGB color space will map to the second NPac vector viathe color lookup table (e.g. HANS lookup table) instead of the firstNPac vector, as done previously.

FIG. 4 shows a non-transitory computer-readable storage medium 400comprising a set of computer-readable instructions 405. Thecomputer-readable storage medium 400 is connectably coupled to aprocessor 410. The processor 410 and the computer-readable storagemedium 400 may be components of a printing system, for example. Theprinting system may comprise a printing system similar to printingsystem 100. The set of computer-readable instructions 405 may beexecuted by the processor 410.

Instruction 415 instructs the processor 410 to receive a color lookuptable comprising a plurality of Neugebauer Primary area coverage (NPac)vectors. The color lookup table may be stored in memory within theprinting system, for example. Alternatively, the color lookup table maybe stored in memory external to the printing system. In examples, theplurality of NPac vectors may correspond respectively to entries in thecolor lookup table. For example, the color lookup table may be a HANSlookup table that maps from a first color space to area coverage space,wherein the plurality of NPac vectors are defined with respect to areacoverage space.

Instruction 420 instructs the processor 410 to determine a firstplurality of Neugebauer Primaries (NPs) based on a given NPac vector inthe color lookup table. For example, the processor 410 may select thegiven NPac vector using the color lookup table. In examples, theprocessor 410 selects an entry in the color lookup table (e.g. HANSlookup table) and reads the corresponding NPac vector in area coveragespace as the given NPac vector. The first plurality of NPs determinedbased on the given NPac vector define a set of colorants associated witha printing process, as previously described.

Instruction 425 instructs the processor 410 to determine a further NPacvector, defining a second plurality of NPs, based on the set ofcolorants and a criterion relating to the printing process. For example,the criterion may comprise increasing or decreasing overprinting, and/orincreasing or decreasing whitespace. Determining the further NPac vectormay be done using an optimization technique, for example LP, RANSAC,and/or Monte Carlo. The optimization may involve defining a solutionspace based on constraints, as described in examples, e.g. each areacoverage component of the generated further NPac vector having a(normalized) value in the range [0, 1]. The optimization may alsoinvolve defining a relation, e.g. an objective function, based onvariables representing a given set of NPs in the intermediate pluralityof NPs and corresponding area coverages. The optimization technique usedmay then determine the set of NPs and corresponding area coverages thatoptimize the relation, e.g. maximize or minimize the objective function,and those NPs and corresponding area coverages may be used to generatethe further NPac vector.

In examples, the processor 410 is instructed to determine anintermediate plurality of NPs based on the set of colorants. Forexample, the processor 410 may generate colorant combinations, e.g. NPs,from the set of colorants defined by the first plurality of NPsassociated with the given NPac vector, as described in examples.Alternatively, as also described in examples, the processor 410 mayselect colorant combinations from a superset, e.g. a “global” valid set,of colorant combinations, the selected colorant combinations comprisingcombinations of the colorants in the set of colorants. For example, ifthe processor 410 determined that the set of colorants defined by thefirst plurality of NPs comprised colorants M, m, and Y (where ‘m’represents light magenta), the processor 410 may proceed to select, fromthe global valid set of NPs, NPs having combinations of the colorants M,m, and Y, e.g. mmY, MYY, YM etc.

In other examples, the processor 410 is instructed to apply a colorantmetric to an intermediate plurality of NPs comprising the valid set ofcolorant combinations when determining the further NPac vector based onthe set of colorants. For example, the colorant metric may be based onthe set of colorants, and may weight a given NP, i.e. colorantcombination, in the valid set based on whether the given NP comprises acolorant not present in the set of colorants defined by the firstplurality of NPs.

Instruction 430 instructs the processor 410 to update the given NPacvector with the further NPac vector in the color lookup table. Forexample, the given NPac vector may correspond to a given entry, or node,in a color lookup table that maps from a given coordinate in a firstcolor space to the given NPac vector in area coverage space. Asdescribed, the color lookup table may be stored in a memory accessibleby the processor 410.

In examples, the processor 410 replaces the given NPac vector with thegenerated further NPac vector, such that the further NPac vectorcorresponds to the given node in the color lookup table that maps fromthe given coordinate in the first color space. Therefore, when the colorlookup table (e.g. HANS lookup table) is used to map the givencoordinate, e.g. by the processor 410 during a printing operation, thegiven coordinate may map to the further NPac vector instead of theoriginal given NPac vector.

In examples, a plurality of NPac vectors in the color lookup table, i.e.corresponding respectively to entries in the color (or HANS) lookuptable, may be updated by a plurality of further NPac vectors generatedby methods as described. For example, the processor 410 may beinstructed by the set of instructions 405 for a plurality of NPacvectors in the color lookup table. Therefore, the color lookup table maybe updated based on the processor 410 updating a plurality of originalNPac vectors to newly generated NPac vectors. For example, the generatedNPac vectors may be determined based on improving a relation betweencomponent NPs and corresponding area coverages subject to constraints.Each generated NPac vector may have an associated colorant-use vectorcorresponding to, for example equivalent to, a colorant-use vectorassociated with a corresponding original in the color lookup table. Incertain cases, all original NPac vectors in the color lookup table, e.g.corresponding to entries in a HANS lookup table mapping from a firstcolor space to area coverage space, are updated with respective NPacvectors that are generated according to examples described herein.

Processor 410 can include a microprocessor, microcontroller, processormodule or subsystem, programmable integrated circuit, programmable gatearray, or another control or computing device. The computer-readablestorage medium 400 can be implemented as one or multiplecomputer-readable storage media. The computer-readable storage medium400 includes different forms of memory including semiconductor memorydevices such as dynamic or static random access memory modules (DRAMs orSRAMs), erasable and programmable read-only memory modules (EPROMs),electrically erasable and programmable read-only memory modules(EEPROMs) and flash memory; magnetic disks such as fixed, floppy andremovable disks; other magnetic media including tape; optical media suchas compact disks (CDs) or digital video disks (DVDs); or other types ofstorage devices. The computer-readable instructions 405 can be stored onone computer-readable storage medium, or alternatively, can be stored onmultiple computer-readable storage media. The computer-readable storagemedium 400 or media can be located either in a printing system orlocated at a remote site from which computer-readable instructions canbe downloaded over a network for execution by the processor 410.

Generating NPac vectors in examples described herein is based on acriterion relating to the printing process. In some examples, thecriterion used may depend on a position of an NPac vector in theoriginal color lookup table. For example, a first region of the colorlookup table may have a first criterion applied when generating NPacvectors to update respective original NPac vectors in the first regionof the color lookup table. A second region of the color lookup table mayhave a second criterion, e.g. different to the first criterion, appliedwhen generating NPac vectors to update respective original NPac vectorsin the second region of the color lookup table. For example, entries inthe color lookup table corresponding to lighter colors in the firstcolor space may have NPac vectors generated, to update original NPacvectors corresponding to said entries, based on a criterion comprisingdecreasing whitespace in the print output. In this example, entries inthe color lookup table corresponding to darker colors in the first colorspace may have NPac vectors generated based on a different criterion,e.g. increasing overprinting.

Certain examples described herein enable a reduction in the number of NPcomponents in an NPac vector having the same determinable colorant-usevector. Consolidating the NPs in this way may allow fewer NPs to eachcover larger areas, which may improve half-toning in the print output.

The preceding description has been presented to illustrate and describeexamples of the principles described. This description is not intendedto be exhaustive or to limit these principles to any precise formdisclosed. Many modifications and variations are possible in light ofthe above teaching.

For example, examples are envisaged where the constraints (thatadjusting, or improving, the relation between the given set of NPs inthe intermediate plurality of NPs is subject to) include a predeterminedmaximum number of NPs used to generate the second NPac vector. Thisconstraint may be a quadratic constraint, in which case non-linearadjustment, e.g. non-linear optimization, of the relation between thegiven set of NPs and associated area coverages may be implemented todetermine the set of NPs and corresponding area coverages to use ingenerating, i.e. to define, the second NPac vector.

What is claimed is:
 1. A method of generating a Neugebauer Primary areacoverage (NPac) vector, comprising: determining a first plurality ofNeugebauer Primaries (NPs) defined by a first NPac vector, the firstplurality of NPs defining a set of characteristics of a printingprocess; generating a second NPac vector defining a second plurality ofNPs, based on: the set of characteristics; and a criterion relating tothe printing process; and providing the second NPac vector for use inprocessing print job data when printing a corresponding print job. 2.The method of claim 1, wherein the set of characteristics defined by thefirst plurality of NPs comprises a set of colorants associated with theprinting process.
 3. The method of claim 2, wherein generating thesecond NPac vector based on the set of characteristics comprisesgenerating colorant combinations from the set of colorants.
 4. Themethod of claim 2, wherein generating the second NPac vector based onthe set of characteristics comprises selecting NPs from a predeterminedplurality of NPs associated with the printing process, the selected NPscorresponding to combinations of colorants in the set of colorants. 5.The method of claim 1, comprising: determining a first colorant-usevector based on the first plurality of NPs and corresponding areacoverages defined by the first NPac vector; and wherein the second NPacvector has an associated second colorant-use vector, the secondcolorant-use vector being determinable based on the second plurality ofNPs and corresponding area coverages defined by the second NPac vector,wherein the second colorant-use vector comprises a same set of componentvalues as the first colorant-use vector.
 6. The method of claim 1,wherein the criterion relates to: overprinting; or whitespace; in aprint output generated using the printing process.
 7. The method ofclaim 1, comprising: applying an imaging metric to an intermediateplurality of NPs comprising the second plurality of NPs, the imagingmetric corresponding to the criterion; determining a relation betweenNPs in a given set of NPs in the intermediate plurality of NPs; anddetermining the second plurality of NPs as a set of NPs from theintermediate plurality of NPs, and corresponding area coverages, basedon the relation; wherein the generating the second NPac vector comprisesgenerating the second NPac vector using the determined second pluralityof NPs and corresponding area coverages.
 8. The method of claim 7,wherein determining the relation between NPs in a given set of NPs inthe intermediate plurality of NPs is based on constraints including: asecond colorant-use vector, determinable based on the second pluralityof NPs and corresponding area coverages defined by the second NPacvector, the second colorant-use vector being equivalent to a firstcolorant-use vector determined based on the first plurality of NPs andcorresponding area coverages defined by the first NPac vector; apredetermined minimum area coverage of each NP defined by the secondNPac vector; a predetermined maximum area coverage of each NP defined bythe second NPac vector; and a predetermined total area coverage of theNPs defined by the second NPac vector.
 9. The method of claim 7, whereindetermining the second plurality of NPs from the intermediate pluralityof NPs, and corresponding area coverages, comprises applying: a linearprogramming (LP) method; a random sample consensus (RANSAC) method; or aMonte Carlo method.
 10. The method of claim 1, further comprisingupdating an entry in a color lookup table that maps to the first vectorto, instead, map to the second vector.
 11. The method of claim 10,further comprising applying a color mapping of the color lookup table toprint job data.
 12. The method of claim 10, further comprising:preparing different versions of the color lookup table using the secondvector; and selecting a version of the color lookup table to apply toprint job data based a parameter of the print job data.
 13. The methodof claim 12, wherein the parameter of the print job data comprises aparameter specifying increased or decreased overprinting.
 14. A printingsystem comprising: a printing device to apply a print material to aprint target in a printing process; a memory storing a color lookuptable to map between color spaces; and a print controller to generate avector in area coverage space, the vector defining a statisticaldistribution of colorant combinations over an area of a halftone, by:selecting from the color lookup table a first vector in area coveragespace; determining a first plurality of colorant combinations based onthe first vector, the first plurality of colorant combinations defininga set of colorants associated with the printing process; and generatinga second vector in area coverage space, defining a second plurality ofcolorant combinations, based on the set of colorants and a criterionrelating to the printing process.
 15. The printing system of claim 14,wherein the generating the second vector is based on a relationinvolving a given set of colorant combinations in an intermediateplurality of colorant combinations, the intermediate pluralitycomprising the second plurality of colorant combinations, andcorresponding area coverages, wherein a metric is applied to the givenset of colorant combinations, the metric based on the criterion.
 16. Theprinting system of claim 15, wherein generating the second vector basedon the relation comprises applying a constraint wherein a secondcolorant-use vector, determinable based on the second plurality ofcolorant combinations and corresponding area coverages defining thesecond vector, is equivalent to a first colorant-use vector determinedbased on the colorant combinations and corresponding area coveragesdefined by the first vector.
 17. The printing system of claim 15,wherein the second plurality of colorant combinations and correspondingarea coverages are selected as components of the second vector based onan output value of the relation involving the second plurality ofcolorant combinations and corresponding area coverages as the given setof colorant combinations and corresponding area coverages.
 18. Theprinting system of claim 14, wherein the print controller is to updatethe first vector with the second vector in the color lookup table. 19.The printing system of claim 14, wherein the print controller is toupdate the first vector with the second vector in the color lookup tableby deleting the first vector from a particular memory location andstoring, instead, the second vector at the particular member location.20. A non-transitory computer-readable storage medium comprising a setof computer-readable instructions that, when executed by a processor ofa printing system, cause the processor to: receive a color lookup tablecomprising a plurality of Neugebauer Primary area coverage (NPac)vectors; determine a first plurality of Neugebauer Primaries (NPs) basedon a given NPac vector in the color lookup table, the first plurality ofNPs defining a set of colorants associated with a printing process;determine a further NPac vector, defining a second plurality of NPs,based on the set of colorants and a criterion relating to the printingprocess; and update the given NPac vector with the further NPac vectorin the color lookup table.